Anyone familiar with the Rite I service in the 1979 Book of Common Prayer will likely have heard the phraseology of this 31st Article of Religion in the Eucharist Prayer (emphasis mine):
All glory be to thee, Almighty God, our heavenly Father, for
that thou, of thy tender mercy, didst give thine only Son Jesus
Christ to suffer death upon the cross for our redemption; who
made there, by his one oblation of himself once offered, a full,
perfect, and sufficient sacrifice, oblation, and satisfaction, for
the sins of the whole world; and did institute, and in his holy
Gospel command us to continue, a perpetual memory of that
his precious death and sacrifice, until his coming again.
I always have to be sure to take this paragraph slowly when I am the Celebrant because I get thrown off if I rush through it with so many uses of the word 'oblation.' The word oblation means the making of a prayerful offering. This is actually one of the 7 types of prayer that the Catechism talks about.
As such, here is the Article that speaks to this theology:
XXXI. Of the Oblation of Christ finished upon the Cross
The offering of Christ once made is that perfect redemption, propitiation, and satisfaction, for all the sins of the whole world, both original and actual; and there is none other satisfaction for sin, but that alone. Wherefore the sacrifices of Masses, in the which it was commonly said, that the Priest did offer Christ for the quick and the dead, to have remission of pain or guilt, were blasphemous fables, and dangerous deceits.
This is pretty standard Protestant reactions to the Catholic Eucharistic Theology of the "Sacrifice of the Mass." What exactly is going on in the Eucharist? That's the basic question. Some Episcopal priests do not refer to the Eucharist as "the Mass" or as a sacrifice at all. Being a good Anglo-catholic, I refer to the Eucharist as "the Mass."
In Catholic theology, the Sacrifice of the Mass is defined (according to the Official Catechism of the Catholic Church) as follows:
Catechism 357. What is the Mass?
The Mass is the Sacrifice of the New Law in which Christ, through the ministry of the priest, offers Himself to God in an unbloody manner under the appearances of bread and wine.
Catechism 360. Why is the Mass the same sacrifice as the sacrifice of the cross?
The Mass is the same sacrifice as the sacrifice of the cross because in the Mass the victim is the same, and the principal priest is the same, Jesus Christ.
(a) Christ, though invisible, is the principal minister, offering Himself in the Mass. The priest is the visible and secondary minister, offering Christ in the Mass.
(b) The most important part of the Mass is the Consecration. In the Consecration bread and wine are changed into the body and blood of Christ who then is really present on the altar. Through the priest He offers Himself to God in commemoration of His death on the cross.
(c) The other most important parts of the Mass are the Offertory and the Communion. In the Offertory the priest offers to God the bread and wine that will be changed into the body and blood of Christ. In the Communion the priest and the people receive the body and blood of Our Lord under the appearances of bread and wine.
Archbishop Cranmer really did not care for this understanding of the Sacrifice of the Mass. However, Cranmer did believe it was a sacrifice of sorts, but by a different definition. Cranmer believes, as did the Reformers, that the woes of the Church could be fixed by returning to what the "Early Church" did and believed. As such, I quote from renowned historian JND Kelly's Early Christian Doctrines as to this point that Cranmer was trying to recapture:
"It was natural for early Christians to think of the Eucharist as a sacrifice. The fulfillment of prophecy demanded a solemn Christian offering, and the rite itself was wrapped in the sacrificial atmosphere with which our Lord invested the Last Supper. The words of institution, ‘Do this’ (touto poieite), must have been charged with sacrificial overtones for second-century ears; Justin at any rate understood them to mean, ‘Offer this.’ . . . The bread and wine, moreover, are offered ‘for a memorial (eis anamnasin) of the passion,’ a phrase which in view of his identification of them with the Lord’s body and blood implies much more than an act of purely spiritual recollection" (J. N. D. Kelly, Early Christian Doctrines, 196–7).
As such, Cranmer believed that it was appropriate to believe that the Eucharist was a "sacrifice of praise and thanksgiving" as it says in the Rite I prayer, as was the sacrifice of the Old Testament. Cranmer and the English reformers largely rejected that the Sacrifice of the Mass was a continual re-offering of Jesus on the Cross. Instead, they advocated that "offering of Christ once made is that perfect redemption, propitiation, and satisfaction, for all the sins of the whole world." In other words, the Mass is not a re-offering of Jesus on the Cross but a thanksgiving sacrifice, a praise offering if you will.
But, again, this is a case of Christians assuming they understand what the other group of Christians teach, when in reality, that is not true. The Catholic church does not teach that the Sacrifice of the Mass is a re-offering of the same sacrifice over and over again. In is not, in essence, an offering of a new sacrifice of Jesus every time a priest says the Mass. It is a re-membering, a putting together again of the original sacrifice, as is time itself is compressed into a single instance, as if time in the eternal stands still. So, the teaching is that the sacrifice of the Mass is not a new sacrifice but a timeless and eternal offering to a timeless and eternal God of the events on the Cross that themselves happened in one time and one place.
Protestants never quite get the eternal and changeless nature of the Catholic Sacrifice of the Mass. They view the Eucharist as some sort of worship or remembrance or sacrifice done after the fact in thanksgiving. I actually take some comfort from the Catholic timeless idea of what the Eucharist is, but I know many would disagree.